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This contribution aims to derive a nonlinear FE formulation for large elastic deformation of hyperelastic thin rubber-like elastomeric materials. The formulation accounts for isotropic as well as transversely isotropic rubber-like materials. Besides, with the developed formulation, deformation of incompressible as well as compressible materials can be investigated. The formulation is applicable for in-plane and out-of-plane deformation of thin membranes. Several problems are inspected including uniaxial and equibiaxial extension of rubber, axisymmetric deformation of annular sheet, stretching a perforated rubber, extension of an anisotropic rubber, and inflation of an initially-flat circular and a square membrane. The results show very good agreement compared with those reported in the literature. Moreover, this model is able to model the inflation of initially flat membranes which is not possible to be done by commercial software.
Firouzi et al. (Mon,) studied this question.